Steering Vector Weighting

ABSTRACT

A method is provided. The method includes computing a beamforming weight matrix W; and using the beamforming weight matrix W to transmit and/or receive data. The beamforming matrix W is computed from a weighted channel estimate matrix Formulae (A): and a channel estimation error matrix Formulae (B): the weighted channel estimate matrix Formulae (C): satisfying a condition, and where Ĥ is a channel estimate matrix and ρ is a weighting factor matrix and ∘ denotes a matrix operation. The weighting factor matrix ρ is such that zeroes of the rows or columns of the weighted channel estimate matrix Formulae (C): are moved as compared to zeroes of the rows or columns of the channel estimate matrix Ĥ.

TECHNICAL FIELD

Disclosed are embodiments related to beamforming.

BACKGROUND

In the emerging 5G cellular systems, beamforming and MIMO transmissionwill be central technologies. The reason is that spectral resources arerunning out at low carrier frequencies which leads to a gradualmigration into higher frequency bands, like the millimeter-wave (“mmw”)band. There, beamforming and a use of massive antenna arrays are neededto achieve a sufficient coverage. There is, for example, plenty ofavailable spectrum around 28 GHz and 39 GHz in the US and other markets.This spectrum needs to be exploited to meet the increasing capacityrequirements. The 5G frequency migration is expected to start at 3.5-5GHz, and then continue to these 28 GHz and 39 GHz bands that areexpected to become available in the not-too-distant future.

In the following description, 3GPP terminology for the 4G LTE system isused (unless otherwise noted), since the standardization of the 5Gcounterparts are not yet finalized.

Beamforming and MIMO transmission is a mature subject today. Thissection presents the basics.

To explain the beamforming concept, consider FIG. 1, which shows anidealized, one-dimensional beamforming case. In system 100, if it isassumed that the UE 102 is located far away from the antenna array 104(e.g., found at a base station (BS)), then it follows that thedifference in travel distance from the base station to the UE, betweenadjacent antenna elements, is 1=kλ·sin(θ), where kλ is the antennaelement separation. Here k is the separation factor, which may forexample be 0.5-0.7 in a typical correlated antenna element arrangement.This means that if a reference signal s_(i)e^(−ωt) is transmitted fromthe i-th antenna element, it will arrive at the user equipment (UE)antenna as a weighted sum:

$s_{UE} = {{\sum_{i = 0}^{N - 1}{s_{i}h_{i}e^{j\; {\omega {({t - \frac{il}{c}})}}}}} = {{e^{j\; \omega \; t}{\sum_{i = 0}^{N - 1}{s_{i}h_{i}e^{{- j}\; 2\; \pi \; f_{c}\frac{{ik}\; \lambda \mspace{11mu} \sin {\; \;}\theta}{f_{c}\lambda}}}}} = {e^{j\; \omega \; t}{\sum_{i = 0}^{N - 1}{s_{i}h_{i}{e^{{- j}\; 2\; \pi \; {ik}\mspace{11mu} \sin \mspace{11mu} \theta}.}}}}}}$

Here ω is the angular carrier frequency; h_(i) is the complex channelfrom the i-th antenna element; t is the time; and f_(c) is the carrierfrequency. In the above equation θ and h_(i) are unknown. In case of afeedback solution, the UE therefore needs to search for all complexchannel coefficients h_(i) and the unknown angle θ. For this reason, thestandard defines a codebook of beams in different directions given bysteering vector coefficients like w_(m,i)=e^(−jf(m,i)), where mindicates a directional codebook entry, and where f( ) denotes afunction. The UE then tests each codebook and estimates the channelcoefficients. The information rate achieved for each codebook entry m iscomputed, and the best one defines the direction and channelcoefficients. This is possible since s_(i) is known. The result is thenencoded and reported back to the base station. This provides the basestation with a best direction (codebook entry) and information thatallows it to build up a channel matrix H. This matrix represents thechannel from each of the transmit antenna elements to each of thereceive antenna elements. Typically, each element of H is represented bya complex number.

The channel matrix can then be used for beamforming computations, or thedirection represented by the reported codebook entry can be useddirectly. In case of MIMO transmission, the MIMO beamforming weightmatrix W needs to be determined, so that a best match, e.g. to thecondition WH=I is achieved. I denotes the identity matrix. In case of anexact match, each layer will become independent of other layers. Thisconcept can be applied for single users or multiple users.

The dominating multi-user access technology for 5G is expected to becomesome variant of orthogonal frequency division multiple access (OFDMA).As is well known, this access is associated with a resource grid,divided in time and frequency, as shown in FIG. 2. The resource gridprovides a division in frequency defined by sub-carriers and a divisionin time by OFDM symbols. The product set of a subcarrier and an OFDMsymbol forms a resource element and as in LTE, a time-frequency block ofresource elements forms a resource block. The currently evolving 3GPP NR5G standard recently also defined slots and mini-slots, givingadditional addressing modes of time-frequency resources. Whenmulti-layered (e.g., MIMO) transmission is used, there is one overlaidresource grid per layer, separated by spatial precoding.

Channel reciprocity is a consequence of Maxwell's Equations. Given twonodes equipped with antenna arrays that communicate in a singlefrequency band, the channel reciprocity property means that at any givenpoint in time, the complex channel coefficient between any transmittingantenna element in one node and any receiving antenna element in theother node, is the same (to within a conjugation) in the uplink and thedownlink. The channel matrix hence remains the same (to within aconjugation and transpose) between the antenna arrays of the two nodeswhen the direction of the transmission is reversed. The two nodes maytypically be a UE and an eNB (or gNB in 5G). For reciprocity to hold,the time is assumed to be essentially the same for the two directions oftransmission.

To exploit reciprocity, the channel coefficients can be directlyestimated by the base station (e.g., eNB, gNB) from UE uplinktransmission of known pilot signals, for example so called soundingreference signals, SRSs. The estimated channel can then be used tocompute the combining weight matrix with a selected principle, and thenused for downlink transmission. This works since the uplink and downlinkchannels are the same (to within a conjugate transpose) when reciprocityis valid.

One beamforming technique is known as Reciprocity Assisted Transmission(RAT). The RAT scheme is obtained as a Minimum Mean Square Error (MMSE)solution. To express the requirements on the beamforming weights, adesired situation may be expressed by the equation

ĤW+{tilde over (H)}W=1  (Eq. 1)

where Ĥ is the estimated channel matrix, of size N_(rx) by N_(tx) whereN_(rx) is the total number of receive antennas for all UEs and whereN_(tx) is the number of base station antennas; {tilde over (H)} is thechannel estimation error, which is assumed to have covariance matrix Γ;and I is the identity matrix.

As shown above, (Eq. 1) is valid for an arbitrary number of users andantenna elements. In order to find the beam weights (i.e., to solve forW), an MMSE criterion may be used; one criterion may be, for example,that E{WW*}=I, where W* represents the conjugate transpose (a.k.a.Hermitian transpose) of W (and likewise for other matrices). Using thiscriterion, the MMSE estimate of W becomes

W=Ĥ(ĤĤ*+Γ)⁻¹  (Eq. 2)

Beamforming implies transmitting the same signal from multiple antennaelements of an antenna array with an amplitude and/or phase shiftapplied to the signal for each antenna element. These amplitude/phaseshifts are commonly denoted as the antenna weights and the collection ofthe antenna weights for each of the antennas is a precoding vector.

Different precoding vectors give rise to a beamforming of thetransmitted signal and the weights can be controlled so that the signalsare coherently combining in a certain angle direction as seen from theantenna array in which case it is said that a transmit (Tx) beam isformed in that direction. Hence, in some contexts, when we refer to abeam we are referring to a particular precoding vector (a.k.a.,“beamforming weights”). If the antennas of the array are placed in twodimensions, i.e. in a plane, then the beam can be steered in bothazimuth and elevation directions with respect to the plane perpendicularto the antenna array.

SUMMARY

Embodiments provide for improved ways to address beamformingopportunities that arise in both the high mmw frequency bands and thelower 5G bands, below 6 GHz. A major problem in these contexts arisesfrom so-called phase noise that affects the spatial multidimensionalchannel, that is obtained and estimated in the radio receivers. Thereason can be explained as follows. When antenna arrays with manyelements are used to enhance coverage and capacity, the transmissionlobes and zeroes that arise in the spatial domain become more narrow,meaning that the angular extension of a high gain beam or low gain zerobecomes smaller. The phase noise affecting the angular channelestimation accuracy, however, remains essentially the same. This resultsin an increase of the sensitivity to phase noise, with increasingantenna array size. This means that advanced transmission schemes (suchas RAT) that apply null-forming to reduce interference in e.g.multi-user multiple input multiple output (MU-MIMO) transmission mayfail in cases where the phase noise becomes too high relative to theantenna array size and the applied transmission scheme. A secondaryconsequence is reduced coverage and reduced capacity of the cellularsystem. Accordingly, it is advantageous to mitigate these effects, e.g.by making the transmission schemes less aggressive and thereby morestable. Such stability may e.g. be beneficial for the link adaptationfunctionality that often applies temporal filtering and prediction insupport of the scheduling of data traffic of multiple users in a cell.Embodiments provide such mitigation, and make the transmission scheme(e.g., RAT) less aggressive and thereby more stable.

Embodiments also provide for smoothing the antenna array beam pattern,thereby making the estimated channel quality in different directionsmore stable. Embodiments provide for a modified RAT transmission scheme,e.g. by providing for modifications to the quantities upon which thetransmission scheme is based, such as the so called steering vectors.Additional advantages of embodiments include modifications that can beimplemented with a low computational complexity.

A problem with the basic RAT transmission scheme (which embodimentsaddress) stems from the fact that interfering transmission to one useronto another user is handled by “null-forming” in the estimateddirections of interfered users. (Null-forming means that, essentially,in the estimated directions of interfered users, the beamforming weightsare selected such that the resulting received power of the beam is low.)To illustrate the problem, consider a scenario with 4 TX antennas andone RX antenna per UE. In this example, UE1 is located at θ₁=45 degreesand UE2 is located at at θ₂=−15 degrees relative to the boresight of theantenna. Assuming equal path loss and line-of-sight (LOS) propagation toboth UEs, FIG. 3 illustrates the gain of pre-coded signal to UE1 andUE2, respectively, as a function of angle of arrival (e.g., azimuthangle). For this illustration, half-wavelength element spacing isassumed for the base station antenna elements. As shown in FIG. 2,received power (at the UE) is plotted for each UE (data stream 1corresponding to UE1 and data stream 2 corresponding to UE2) as afunction of the angle of arrival. As seen, received power for UE1reaches a low (or “null”) at θ₂=−15 (i.e. the location of theinterfering UE2); likewise, received power for UE2 reaches a low (or“null”) at θ₁=45 degrees (i.e. the location of the interfering UE1).

As can be seen (e.g., in FIG. 3), in the basic RAT transmission scheme,sharp nulls are placed at the directions of the other (interfering) UEs,e.g. in order to minimize cross-talking interference. However, thisstrategy is non-robust in the presence of channel estimation errors dueto e.g. quantization of the precoding vector over multiple resourceblocks. The consequence is that MU-MIMO performance deteriorates to anunacceptable level.

Embodiments provide for modifications of the basic RAT transmissionscheme, such that: (1) the sharp and narrow nulls are replaced bysmoother nulls; and (2) the associated computational complexity is low.Further, while modifications are discussed with respect to a particulartransmission scheme (e.g., RAT), embodiments are also applicable withrespect to other transmission schemes. In some embodiments, where theangular UE separation becomes comparable to the phase noise level,substantial performance gains over known methods are achievable.

According to a first aspect, a method is provided. The method includescomputing a beamforming weight matrix W; and using the beamformingweight matrix W to transmit and/or receive data. The beamforming matrixW is computed from a weighted channel estimate matrix {hacek over(H)}=ρ∘Ĥ and a channel estimation error matrix {tilde over (H)}, theweighted channel estimate matrix {hacek over (H)} satisfying acondition, and where Ĥ is a channel estimate matrix and ρ is a weightingfactor matrix and ∘ denotes a matrix operation. The weighting factormatrix ρ is such that zeroes of the rows or columns of the weightedchannel estimate matrix {hacek over (H)} are moved as compared to zeroesof the rows or columns of the channel estimate matrix Ĥ.

In embodiments, the matrix operation ∘ denotes the Hadamard matrixproduct. In embodiments, the condition that the weighted channelestimate matrix {hacek over (H)} satisfies is {hacek over (H)}W+{tildeover (H)}W=I, where I is the identity matrix. In embodiments, computingthe beamforming weight matrix W includes estimating W based on a minimummean squares error (MMSE) approximation method, and the estimateW={hacek over (H)}({hacek over (H)}{hacek over (H)}*+Γ)⁻¹, where {hacekover (H)}* denotes the Hermitian of {hacek over (H)} and Γ is acovariance matrix of the channel estimation error matrix {tilde over(H)}, and where an MMSE criterion E{WW*}=I is used, E being thestatistical expected value operator.

In embodiments, the weighting factor matrix

$\rho = {\quad\begin{pmatrix}1 & \rho & \ldots & \rho^{N_{tx} - 1} \\\vdots & \vdots & \ddots & \vdots \\1 & \rho & \ldots & \rho^{N_{tx} - 1}\end{pmatrix}}$

where ρ has dimension N_(rx) by N_(tx), where N_(rx) is the number ofreceive antennas and N_(tx) is the number of base station antennas, andρ is a scalar. In embodiments, the weighting factor

$\rho = {\quad\begin{pmatrix}1 & \rho_{1} & \ldots & \rho_{N_{rx}}^{N_{tx} - 1} \\\vdots & \vdots & \ddots & \vdots \\1 & \rho_{N_{rx}} & \ldots & \rho_{N_{rx}}^{N_{tx} - 1}\end{pmatrix}}$

where ρ has dimension N_(rx) by N_(tx), where N_(rx) is the number ofreceive antennas and N_(tx) is the number of base station antennas, andeach ρ_(i) is a scalar. In embodiments, an absolute value of ρ and/orρ_(i) is strictly less than 1. In embodiments, an absolute value of ρand/or ρ_(i) is strictly greater than 1. In embodiments, an absolutevalue of ρ_(i) is strictly less than 1 for a first set of values and anabsolute value of ρ_(i) is strictly greater than 1 for a second set ofvalues, wherein the first and second sets of values are disjoint andinclude all values of 1≤i≤N_(rx). In embodiments, computing thebeamforming weight matrix W employs a Reciprocity Assisted Transmission(RAT) algorithm.

According to a second aspect, a device is provided. The device isadapted to compute a beamforming weight matrix W; and use thebeamforming weight matrix W to transmit and/or receive data. Thebeamforming matrix W is computed from a weighted channel estimate matrix{hacek over (H)}=ρ∘Ĥ and a channel estimation error matrix {tilde over(H)}, the weighted channel estimate matrix {hacek over (H)} satisfying acondition, and where Ĥ is a channel estimate matrix and ρ is a weightingfactor matrix and ∘ denotes a matrix operation. The weighting factormatrix ρ is such that zeroes of the rows or columns of the weightedchannel estimate matrix {hacek over (H)} are moved as compared to zeroesof the rows or columns of the channel estimate matrix Ĥ.

According to a third aspect, a device is provided. The device includes acomputing module configured to compute a beamforming weight matrix W;and a transceiver module configured to use the beamforming weight matrixW to transmit and/or receive data. The beamforming matrix W is computedfrom a weighted channel estimate matrix {hacek over (H)}=ρ∘Ĥ and achannel estimation error matrix {tilde over (H)}, the weighted channelestimate matrix {hacek over (H)} satisfying a condition, and where Ĥ isa channel estimate matrix and ρ is a weighting factor matrix and ∘denotes a matrix operation. The weighting factor matrix ρ is such thatzeroes of the rows or columns of the weighted channel estimate matrix{hacek over (H)} are moved as compared to zeroes of the rows or columnsof the channel estimate matrix Ĥ.

According to a fourth aspect, a computer program is provided. Thecompute program includes instructions which, when executed on at leastone processor, causes the at least one processor to carry out the methodaccording to any one of the embodiments of the first aspect.

According to a fifth aspect, a carrier is provided. The carrier includesthe computer program of the fourth aspect. The carrier is one of anelectronic signal, optical signal, radio signal or computer readablestorage medium.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated herein and form partof the specification, illustrate various embodiments.

FIG. 1 illustrates shows an idealized, one-dimensional beamforming case.

FIG. 2 illustrates a resource grid, divided in time and frequency.

FIG. 3 illustrates a graph according to some embodiments.

FIG. 4 illustrates a graph according to some embodiments.

FIG. 5 illustrates a graph according to some embodiments.

FIG. 6 illustrates a graph according to some embodiments.

FIG. 7 illustrates a flow chart according to some embodiments.

FIG. 8 is a diagram showing functional modules of a device according tosome embodiments.

FIG. 9 is a block diagram of a device according to some embodiments.

DETAILED DESCRIPTION

As discussed above, a problem with the basic RAT transmission scheme isthat it is non-robust and that null-forming can lead to sharp and narrownulls. One reason for this is because null-forming amounts to placingzeroes on the unit circle that represents the directions to the otherUEs. Such zeroes, placed exactly on the unit circle, can lead to anantenna gain that is exactly 0 in exactly the estimated interferingdirection. However, this also results in the antenna gain zeroesbecoming extremely deep and narrow in the angular dimension, andtherefore the zeroes become extremely sensitive to angular modelingerrors like beam weight quantization errors and phase noise intransmitters and receivers. In addition, channel estimation errors interms of the phase affects the performance of the resulting beams.

The presence of zeroes on the unit circle means that a polynomialassociated with the precoding vector (i.e. where the precoding vector isviewed as a spatial polynomial having coefficients corresponding to theprecoding vector elements), also has zeroes on the unit circle. This inturn means that polynomials associated with the channel matrix (i.e.where the polynomials have coefficients corresponding to the channelmatrix elements) have zeroes on the unit circle. Embodiments attempt tobroaden the nulls provided by null-forming in order to create morerobust, predictable behavior. Specifically, embodiments provide for amodified channel matrix such that the zeroes of the polynomialassociated with the modified channel matrix are moved inside the unitcircle (or outside), i.e. the zeroes are moved to another circle withradius strictly less (or greater) than one. This ensures that there isalways a final distance in the complex plane from the unit circle to thezero which prevents an exactly zero antenna gain corresponding to thezero of the associated polynomial.

The idea of null-forming amounting to placing zeroes on the unit circleis well understood in the field. A fuller explanation of this, and theeffect of moving the zeroes inside (or outside) the unit circle isoffered further below.

A weighting factor matrix ρ (for modifying a steering vector matrix W)is defined as follows:

$\begin{matrix}{\rho = {\quad\begin{pmatrix}1 & \rho_{1} & \ldots & \rho_{1}^{N_{tx} - 1} \\\vdots & \vdots & \ddots & \vdots \\1 & \rho_{N_{rx}} & \ldots & \rho_{N_{rx}}^{N_{tx} - 1}\end{pmatrix}}} & ( {{Eq}.\mspace{14mu} 3} ) \\{\rho = {\quad\begin{pmatrix}1 & \rho & \ldots & \rho^{N_{tx} - 1} \\\vdots & \vdots & \ddots & \vdots \\1 & \rho & \ldots & \rho^{N_{tx} - 1}\end{pmatrix}}} & ( {{Eq}.\mspace{14mu} 4} )\end{matrix}$

where ρ or each of the ρ_(i) is a non-zero scalar. (As can be seen, (Eq.4) is a special case of (Eq. 3) where ρ_(i)=ρ for all values of0≤i≤N_(rx). Also, note that the matrix ρ is denoted by boldface, whilethe weighting factor ρ or ρ_(i) is an element of the matrix ρ.)

This matrix (i.e. φ has dimension N_(rx) by N_(tx) and the weightingfactor ρ_(i) typically meets |ρ_(i)|<1 (or |ρ_(i)|>1). The weightedchannel matrix is then given by {hacek over (H)}=ρ∘Ĥ, where ∘ denotesthe Hadamard matrix product (e.g., in its simplest form expressingelement-wise matrix multiplication). The weighted channel matrix ({hacekover (H)}) can then be substituted for the unweighted version (Ĥ) in(Eq. 2), resulting in:

W={hacek over (H)}({hacek over (H)}{hacek over (H)}*+Γ)¹  (Eq. 5)

FIGS. 4-5 illustrate advantages to using this weighted channel matrix.These figures continue the example of FIG. 3, where UE1 is located atθ₁=45 degrees and UE2 is located at θ₂=−15 degrees relative to theboresight of the antenna. In FIG. 4, showing the data streamcorresponding to UE1, the null located at θ₂=−15 degrees is smoothed forvalues of ρ=0.7, 0.8, and/or 0.9, relative to unity (i.e. unweighted).Likewise, in FIG. 5, showing the data stream corresponding to UE2, thenull located at θ₁=45 degrees is smoothed for values of p=0.7, 0.8,and/or 0.9, relative to unity (i.e. unweighted).

Values |ρ|>1 would have a similar effect, and embodiments also use suchvalues. In embodiments, different values of ρ for the weighted channelmatrix may be used based on the particular subcarrier that thebeamforming weights are being computed for. For instance, values of|ρ|>1 may be used for some subcarriers, and values of |ρ|<1 may be usedfor others. Likewise, where the matrix ρ is based on (Eq. 3), theexpression |ρ_(i)|<1 may hold for some values of i, and the expression|ρ_(i)|>1 may hold for other values of i. Mixing up, or varying, thevalue of ρ or ρ_(i) in this manner may improve the general balancing ofthe beamforming computations. For example, numerical properties may beimproved; that is, such mixing may create a wider range of values forthe matrix, avoiding all the elements being smaller (for small values of|p|) or larger (for large values of |ρ|), which may have beneficialeffects in some embodiments.

By using the weighting factor matrix ρ, zeroes (or nulls) are moved fromthe unit circle. In contrast, if a diagonal matrix e.g. for“regularization” were used instead, there would still be nulls on theunit circle, which would still lead to the problems identified above.Now that the weighting factor matrix has been introduced, the concept ofmoving zeroes (or nulls) from the unit circle will be explained in moredetail.

Starting with the element-wise multiplication by ρ, and then factoringout the complex phase shifting caused by the antenna array timedifference between elements, the product ρ∘Ĥ can be expressed, for onerow i, by an expression of the form

Ĥ _({i,0}) +ρĤ _({i,1}) e ^(jQ)+ρ² Ĥ _({i,2}) e ^(2jQ)+ . . . +ρ^(N)^(tx) ⁻¹ Ĥ _({i,N) _(tx) _(-1}) e ^((N) ^(tx) ^(-1)jQ)

where Q represents a complex phase shifting factor, and j is theimaginary unit √{square root over (−1)}.

Now, letting z=e^(jQ), the expression above takes the form

Ĥ _({i,0}) +ρĤ _({i,1}) z+ρ ² Ĥ _({i,2}) z ²+ . . . +ρ^(N) ^(tx) ⁻¹ Ĥ_({i,N) _(tx) _(-1}) z ^((N) ^(tx) ⁻¹⁾

which is a polynomial in z. The roots of this expression may be referredto as “zeroes,” such as the zeroes that are discussed throughout thisapplication. It is possible to refer to zeroes of rows or columns of theweighted channel estimate matrix. This is so because if we switchnotation to one where we have transmit antennas indexed while going downa column (instead of a row i as illustrated above), then we get columns(instead of rows) and these equations are transposed.

Continuing with this notation, and applying it to the MMSE equationabove (Eq. 2), results in the expression

W={hacek over (H)}(z)({hacek over (H)}(z){hacek over (H)}*(z)+Γ)⁻¹

(That is, the matrices {hacek over (H)} and {hacek over (H)}* can beconsidered as functions of the variable z previously introduced.) Sincematrix inversion is essentially just a more complicated form ofdivision, it follows that Ĥ is a factor of W. In some circumstances,there may be some cancellation due Γ, however requiring that Γ>0 willprevent most such cancellation issues. This means that, typically, thezeroes of W are the same as those of Ĥ.

In cases where the channel is flat with all channel elements being thesame, and we let ρ=1, then we can solve for the zeroes. Doing so, we get(for two representative values of N_(tx)):

1+z=0→z:=1 for N _(tx)=2

1+z+z ²=0→z:=−½±√{square root over (¾)}j for N _(tx)=3

where the zeroes here (for ρ=1) are all on the unit circle.

For the same case where the channel is flat, but now letting ρ<1, we get(for two representative values of N_(tx)):

$\begin{matrix}{{1 + {\rho \; z}} = { 0arrow z :={- \frac{1}{\rho}}}} & {{{for}\mspace{14mu} N_{tx}} = 2} \\{{1 + {\rho z} + {\rho^{2}z^{2}}} = { 0arrow{z:}  = {{- \frac{1}{2\rho}} \pm {\frac{1}{\rho}\sqrt{\frac{3}{4}}j}}}} & {{{for}\mspace{14mu} N_{tx}} = 3}\end{matrix}$

where the zeroes here (for ρ<1) are all at a distance 1/ρ from the unitcircle.

FIG. 6 illustrates a chart graphing angle of departure versusthroughput, according to some embodiments. As shown, different values ofρ (0.9, 0.95, and 1) with different signal-to-noise ratios (0 dB and ±10dB) are shown. The chart shows throughput using a modified RATtransmission scheme as described herein, and shows how this schemeaffects the downlink capacity. To generate the graph, a combined linkand system simulator was used. The simulator includes the completereciprocity based beamforming chain in the eNB/gNB including channelestimation, link adaptation, outer loop, scheduling, beamformingcomputation, and modulation-and-coding scheme (MCS) selection. It alsoincludes radio propagation modeling and modeling of the UEs.Specifically, the simulation used a scenario having where the eNB/gNBincluded 16 antenna elements and where the UEs each included 2 antennaelements. The angular UE separation was varied. It can be noted that (i)the theoretical maximum throughput is achieved when the antennaseparation becomes large for high SNRs, and (ii) the performance isalways better with weighting than without.

Finally note that the above represents a rank 1 (per UE) transmissioncase. This is the reason why two antennas in the UEs are enough toseparate two data streams. In case of rank 2 transmission, the UEs wouldneed four antennas in order to separate four data streams, and so on.

FIG. 7 is a flow chart according to exemplary embodiments. Process 700is a method that may be performed, for example, by a base station, suchas an eNB or gNB and/or by radio processing circuitry. The methodincludes computing a beamforming weight matrix W (step 702). The methodfurther includes using the beamforming weight matrix W to transmitand/or receive data (step 704). The beamforming matrix W is computedfrom a weighted channel estimate matrix {hacek over (H)}=ρ∘Ĥ and achannel estimation error matrix {tilde over (H)}, the weighted channelestimate matrix {hacek over (H)} satisfying a condition, and where Ĥ isa channel estimate matrix and ρ is a weighting factor matrix and ∘denotes a matrix operation (step 706). The weighting factor matrix ρ issuch that zeroes of the rows or columns of the weighted channel estimatematrix {hacek over (H)} are moved as compared to zeroes of the rows orcolumns of the channel estimate matrix Ĥ (step 708).

In some embodiments, the matrix operation ∘ denotes the Hadamard matrixproduct. In embodiments, the condition that the weighted channelestimate matrix {hacek over (H)} satisfies is {hacek over (H)}W+{tildeover (H)}W=I, where I is the identity matrix. In embodiments, computingthe beamforming weight matrix W comprises estimating W based on aminimum mean squares error (MMSE) approximation method, and wherein theestimate W={hacek over (H)}({hacek over (H)}{hacek over (H)}*+Γ)⁻¹,where {hacek over (H)}* denotes the Hermitian of {hacek over (H)} and Γis a covariance matrix of the channel estimation error matrix {tildeover (H)}, and where an MMSE criterion E{WW*}=I is used, E being thestatistical expected value operator.

In some embodiments, the weighting factor matrix

$\rho = {\quad\begin{pmatrix}1 & \rho & \ldots & \rho^{N_{tx} - 1} \\\vdots & \vdots & \ddots & \vdots \\1 & \rho & \ldots & \rho^{N_{tx} - 1}\end{pmatrix}}$

where ρ has dimension N_(rx) by N_(tx), where N_(rx) is the number ofreceive antennas and N_(tx) is the number of base station antennas, andρ is a scalar. In embodiments, the weighting factor

$\rho = {\quad\begin{pmatrix}1 & \rho_{1} & \ldots & \rho_{1}^{N_{tx} - 1} \\\vdots & \vdots & \ddots & \vdots \\1 & \rho_{N_{rx}} & \ldots & \rho_{N_{rx}}^{N_{tx} - 1}\end{pmatrix}}$

where ρ has dimension N_(rx) by N_(tx), where N_(rx) is the number ofreceive antennas and N_(tx) is the number of base station antennas, andeach ρ_(i) is a scalar. In embodiments, an absolute value of ρ and/orρ_(i) is strictly less than 1 (or strictly greater than 1). Inembodiments, an absolute value of ρ_(i) is strictly less than 1 for afirst set of values and an absolute value of ρ_(i) is strictly greaterthan 1 for a second set of values, wherein the first and second sets ofvalues are disjoint and include all values of 1≤i≤N_(rx).

In embodiments, computing the beamforming weight matrix W employs aReciprocity Assisted Transmission (RAT) algorithm.

FIG. 8 is a diagram showing functional modules of a device 104 accordingto some embodiments. As shown in FIG. 8, device 104 includes a computingmodule 802 and a transceiver module 804. The computing module isconfigured to compute a beamforming weight matrix W; and the transceivermodule is configured to use the beamforming weight matrix W to transmitand/or receive data. The beamforming matrix W is computed from aweighted channel estimate matrix {hacek over (H)}=ρ∘Ĥ and a channelestimation error matrix {tilde over (H)}, the weighted channel estimatematrix {hacek over (H)} satisfying a condition, and where Ĥ is a channelestimate matrix and ρ is a weighting factor matrix and ∘ denotes amatrix operation. The weighting factor matrix ρ is such that zeroes ofthe rows or columns of the weighted channel estimate matrix {hacek over(H)} are moved as compared to zeroes of the rows or columns of thechannel estimate matrix Ĥ

FIG. 9 is a block diagram of a device 104 according to some embodiments.As shown in FIG. 9, device 104 may comprise: a data processing apparatus(DPA) 902, which may include one or more processors (P) 955 (e.g., ageneral purpose microprocessor and/or one or more other processors, suchas an application specific integrated circuit (ASIC), field-programmablegate arrays (FPGAs), and the like); a network interface 948 comprising atransmitter (Tx) 945 and a receiver (Rx) 947 for enabling device 104 totransmit data to and receive data from other nodes connected to anetwork 910 (e.g., an Internet Protocol (IP) network) to which networkinterface 948 is connected; circuitry 903 (e.g., radio transceivercircuitry) coupled to an antenna system 904 for wireless communicationwith UEs); and local storage unit (a.k.a., “data storage system”) 908,which may include one or more non-volatile storage devices and/or one ormore volatile storage devices (e.g., random access memory (RAM)). Inembodiments where device 104 includes a general purpose microprocessor,a computer program product (CPP) 941 may be provided. CPP 941 includes acomputer readable medium (CRM) 942 storing a computer program (CP) 943comprising computer readable instructions (CRI) 944. CRM 942 may be anon-transitory computer readable medium, such as, but not limited, tomagnetic media (e.g., a hard disk), optical media, memory devices (e.g.,random access memory, flash memory), and the like. In some embodiments,the CRI 944 of computer program 943 is configured such that whenexecuted by data processing apparatus 902, the CRI causes device 104 toperform steps described above (e.g., steps described above withreference to the flow charts). In other embodiments, device 104 may beconfigured to perform steps described herein without the need for code.That is, for example, data processing apparatus 902 may consist merelyof one or more ASICs. Hence, the features of the embodiments describedherein may be implemented in hardware and/or software.

While various embodiments of the present disclosure are described herein(including the appendices, if any), it should be understood that theyhave been presented by way of example only, and not limitation. Thus,the breadth and scope of the present disclosure should not be limited byany of the above-described exemplary embodiments. Moreover, anycombination of the above-described elements in all possible variationsthereof is encompassed by the disclosure unless otherwise indicatedherein or otherwise clearly contradicted by context.

Additionally, while the processes described above and illustrated in thedrawings are shown as a sequence of steps, this was done solely for thesake of illustration. Accordingly, it is contemplated that some stepsmay be added, some steps may be omitted, the order of the steps may bere-arranged, and some steps may be performed in parallel.

1-14. (canceled)
 15. A method comprising: computing a beamforming weightmatrix W; and using the beamforming weight matrix W to transmit orreceive data; wherein the beamforming matrix W is computed from aweighted channel estimate matrix {hacek over (H)}=ρ∘Ĥ and a channelestimation error matrix {tilde over (H)}, the weighted channel estimatematrix {hacek over (H)} satisfying a condition, and where Ĥ is a channelestimate matrix and ρ is a weighting factor matrix and ∘ denotes amatrix operation; and wherein the weighting factor matrix ρ is such thatzeroes of the rows or columns of the weighted channel estimate matrix{hacek over (H)} are moved as compared to zeroes of the rows or columnsof the channel estimate matrix Ĥ.
 16. The method of claim 15, whereinthe matrix operation ∘ denotes the Hadamard matrix product.
 17. Themethod of claim 15, wherein the condition that the weighted channelestimate matrix {hacek over (H)} satisfies is {hacek over (H)}W+{tildeover (H)}W=I, where I is the identity matrix.
 18. The method of claim15, wherein computing the beamforming weight matrix W comprisesestimating W based on a minimum mean squares error (MMSE) approximationmethod, and wherein the estimate W={hacek over (H)}({hacek over(H)}{hacek over (H)}*+Γ)⁻¹, where {hacek over (H)}* denotes theHermitian of {hacek over (H)} and Γ is a covariance matrix of thechannel estimation error matrix {tilde over (H)}, and where an MMSEcriterion E{WW*}=I is used, where E is the statistical expected valueoperator.
 19. The method of claim 15, wherein the weighting factormatrix $\rho = {\quad\begin{pmatrix}1 & \rho & \ldots & \rho^{N_{tx} - 1} \\\vdots & \vdots & \ddots & \vdots \\1 & \rho & \ldots & \rho^{N_{tx} - 1}\end{pmatrix}}$ where ρ has dimension N_(rx) by N_(tx), where N_(rx) isthe number of receive antennas and N_(tx) is the number of base stationantennas, and ρ is a scalar.
 20. The method of claim 15, wherein theweighting factor $\rho = {\quad\begin{pmatrix}1 & \rho_{1} & \ldots & \rho_{N_{rx}}^{N_{tx} - 1} \\\vdots & \vdots & \ddots & \vdots \\1 & \rho_{N_{rx}} & \ldots & \rho_{N_{rx}}^{N_{tx} - 1}\end{pmatrix}}$ where ρ has dimension N_(rx) by N_(tx), where N_(rx) isthe number of receive antennas and N_(tx) is the number of base stationantennas, and each ρ_(i) is a scalar.
 21. The method of claim 19,wherein an absolute value of at least one of ρ or ρ_(i) is strictly lessthan
 1. 22. The method of claim 19, wherein an absolute value of atleast one of ρ and ρ_(i) is strictly greater than
 1. 23. The method ofclaim 20, wherein an absolute value of ρ_(i) is strictly less than 1 fora first set of values and an absolute value of ρ_(i) is strictly greaterthan 1 for a second set of values, wherein the first and second sets ofvalues are disjoint and include all values of 1≤i≤N_(rx).
 24. The methodof claim 15, wherein computing the beamforming weight matrix W includesusing a Reciprocity Assisted Transmission (RAT) algorithm.
 25. A devicecomprising: radio transceiver circuitry; and radio processing circuitryconfigured to: compute a beamforming weight matrix W; and use thebeamforming weight matrix W to transmit or receive data via thetransceiver circuitry; wherein the beamforming matrix W is computed froma weighted channel estimate matrix {hacek over (H)}=ρ∘Ĥ and a channelestimation error matrix {tilde over (H)}, the weighted channel estimatematrix {hacek over (H)} satisfying a condition, and where Ĥ is a channelestimate matrix and ρ is a weighting factor matrix and ∘ denotes amatrix operation; and wherein the weighting factor matrix ρ is such thatzeroes of the rows or columns of the weighted channel estimate matrix{hacek over (H)} are moved as compared to zeroes of the rows or columnsof the channel estimate matrix Ĥ.
 26. A non-transitory computer-readablestorage medium storing computer program instructions which, whenexecuted by at least one processor of a device, cause the device to:compute a beamforming weight matrix W; and use the beamforming weightmatrix W to transmit or receive data; wherein the beamforming matrix Wis computed from a weighted channel estimate matrix {hacek over (H)}=ρ∘Ĥand a channel estimation error matrix {tilde over (H)}, the weightedchannel estimate matrix {hacek over (H)} satisfying a condition, andwhere Ĥ is a channel estimate matrix and ρ is a weighting factor matrixand ∘ denotes a matrix operation; and wherein the weighting factormatrix ρ is such that zeroes of the rows or columns of the weightedchannel estimate matrix {hacek over (H)} are moved as compared to zeroesof the rows or columns of the channel estimate matrix Ĥ.